Analysis of the formation of ion beams in varying electric fields of a stationary plasma thruster

We propose a technique for analyzing the distribution function of the velocity components (radial V _r and azimuthal V _φ) of ions in a beam. This technique is used for studying the ion beam emerging from a stationary plasma thruster (SPT). It is shown that the beam contains ions with a radial velocity component in the range V _r /V _z = ? 1.2 to +0.74, as well as ions with the azimuthal velocity component in the range V _?/V _z = ±0.9. Numerical calculations lead to the conclusion that ions acquire the azimuthal velocity component in the field of the azimuthal wave of the plasma potential evolving in the SPT channel.     

Velocity encoding and velocity compensation for multi-spoke RF excitation

PurposeTo investigate velocity encoded and velocity compensated variants of multi-spoke RF pulses that can be used for flip-angle homogenization at ultra-high fields (UHF). Attention is paid to the velocity encoding for each individual spoke pulse and to displacement artifacts that arise in Fourier transform imaging in the presence of flow.Theory and methodsA gradient waveform design for multi-spoke excitation providing an algorithm for minimal TE was proposed that allows two different encodings. Such schemes were compared to an encoding approach that applies an established scheme to multi-spoke excitations. The impact on image quality and quantitative velocity maps was evaluated in phantoms using single- and two-spoke excitations. Additional validation measurements were obtained in-vivo at 7 T.ResultsPhantom experiments showed that keeping the first gradient moment constant for all k-space lines eliminates any displacements in phase-encoding and slice-selection direction for all spoke pulses but leads to artifacts for non-zero velocity components along readout direction. Introducing variable but well-defined first gradient moments in the phase-encoding direction creates displacements along the velocity vector and thus minimizes velocity-induced geometrical distortions. Phase-resolved mean volume flow in the ascending and descending aorta obtained from two-spoke excitation showed excellent agreement with single-spoke excitation over the cardiac cycle (mean difference 0.8 ± 16.2 ml/s).ConclusionsThe use of single- and multi-spoke RF pulses for flow quantification at 7 T with controlled displacement artifacts has been successfully demonstrated. The presented techniques form the basis for correct velocity quantification and compensation not only for conventional but also for multi-spoke RF pulses allowing in-plane B₁⁺ homogenization using parallel transmission at UHF.     

Detailed unsteady dynamics of flame-flow interactions during combustion instability and its transition scenario for lean-premixed low-swirl hydrogen turbulent flames

This experimental study elucidates the unsteady dynamics of flame-flow interactions during unique thermoacoustic instability (TI) and the transition mechanism from stable combustion to TI for lean-premixed hydrogen turbulent jet flames in a low-swirl combustor (LSC), where a swirler assembly consists of an unswirled central region (CR) and an annular swirler region (SR). Simultaneous 200-kHz pressure fluctuation p’ measurements and 10-kHz OH* chemiluminescence imaging, as well as 40-kHz stereoscopic particle image velocimetry (SPIV) and two-dimensional PIV measurements for steady-state and transient data acquisitions, respectively, were conducted. The SPIV was performed in multiple planes to explore three-dimensional velocity fields. During TI, periodic flashback was possibly caused by significant axial velocity oscillations, resulting in the local mixture velocity falling below the turbulent flame speed. The large-scale vortex ring generated by the velocity oscillations caused axisymmetric radial velocity V_r oscillations with switching signs during the TI period. Similar to a typical low-swirl flow, the positive V_r away from the combustor axis created diverging flow, whereas unlike the typical flowfield, the negative V_r toward the combustor axis generated converging flow while flattening the axial velocity distributions, which was the signature phenomenon for this TI. Using the transient data and dynamic mode decomposition, variations in delay times between the mixture injection and its convection to a region with positive local Rayleigh indices were investigated. During stable combustion, the mixture jet from the SR predominantly induced thermoacoustic coupling (TC). As the combustion transitioned into the TI, the mixture jet from the CR began to induce TC and, eventually, achieved predominance in inducing TC during fully evolved TI. The transition from the SR jet- into CR jet-dominant TI arising from the dynamic flame-flow interactions resulted from the inherent physical characteristics of hydrogen flames, thereby yielding the larger p’ amplitude compared to typical TIs.     

Extrapolation from positive to negative energy of the Woods-Saxon parametrization of the n-208Pb mean field

The real part V(r); E) of the nucleon-nucleus mean field is assumed to have a Woods-Saxon shape, and accordingly to be fully specified by three quantities: the potential depth U_v(E), radius R_V(E) and diffuseness a_v(E). At a given nucleon energy E these parameters can be determined from three different radial moments [r^q]_v = (4π/A) ∝V(r; E)r^q dr. This is useful because a dispersion relation approach has recently been developed for extrapolating [r^q]_V(E) from positive to negative energy, using as inputs the radial moments of the real and imaginary parts of empirical optical-model potentials V(r; E) + iW(r; E). In the present work, the values of U_v(E), R_v(E) and a_v(E) are calculated in the case of neutrons in ²⁰⁸Pb in the energy domain −20 < E < 40 MeV from the values of [r^q]_V(E) for q = 0.8, 2 and 4. It is found that both U_V(E) and R_v(E) have a characteristic energy dependence. The energy dependence of the diffuseness a_a(E) is less reliably predicted by the method. The radius R_V(E) increases when E decreases from 40 to 5 MeV. This behaviour is in agreement with empirical evidence. In the energy domain −10 MeV < E < 0, R_V(E) is predicted to decrease with decreasing energy. The energy dependence of the root mean square radius is similar to that of R_V(E). The potential depth U_v slightly increases when E decreases from 40 to 15 MeV and slightly decreases between 10 and 5 MeV; it is consequently approximately constant in the energy domain 5 < E < 20 MeV, in keeping with empirical evidence. The depth U_v increases linearly with decreasing E in the domain −10 MeV < E < 0. These features are shown to persist when one modifies the detailed input of the calculation, namely the empirical values of [r^q]_v(E) for E > 0 and the parametrization [r_q]_w(E) of the energy dependence of the radial moments of the imaginary part of the empirical optical-model potentials. In the energy domain −10 MeV < E < 0, the calculated V(r; E) yields good agreement with the experimental single-particle energies; the model thus accurately predicts the shell-model potential (E < 0) from the extrapolation of the optical-model potential (E > 0). In the dispersion relation approach, the real part V(r; E) is the sum of a Hartree-Fock type contribution V_HF(r; E) and of a dispersive contribution ΔV(r; E). The latter is due to the excitation of the ²⁰⁸Pb core. The dispersion relation approach enables the calculation of the radial moment [r^q]_ΔV(E) from the parametrization [r^q]_w(E): several schematic models are considered which yield algebraic expressions for [r^q]_ΔV(E). The radial moments [r^q]_HF(E) are approximated by linear functions of E. When in addition, it is assumed that V_HF(r; E) has a Woods-Saxon radial shape, the energy dependence of its potential parameters (U_HF, R_HF, a_HF) can be calculated. Furthermore, the values of ΔV(r; E) can then be derived. It turns out that ΔV(r; E) is peaked at the nuclear surface near the Fermi energy and acquires a Woods-Saxon type shape when the energy increases, in keeping with previous qualitative estimates. It is responsible for the peculiar energy dependence of R_V(E) in the vicinity of the Fermi energy.     

A theorem on the order of levels in confining potentials

We prove that in a two-body, non-relativistic system interacting via a potential V = ?g²/r + V_c(r), where V_c is a confining potential non-singular at the origin, the 2S level is above the 2P level if V_c satisfies the following sufficient condition: This covers the well-known cases of linear potentials or harmonic oscillator potentials, which were considered in charmonium models, but also more generally, for instance, V_c(r) = r^α, α >0.     

The inner charge defect method as an analog to the quantum defect method

A method is proposed for the calculation of one-electron wave functions for excited bound and free atomic states. For the interaction potential between the outer electron and the atomic core, we have adopted the following potential: V(r) = q₀/r for r < r₀ and V(r) = -1/r for r > r₀, where r₀ is approximately equal to the core radius, q₀(∈, 1) = Δq + 1, and Δq > 0 is the inner charge defect. It is shown, for atomic argon, that the method has about the same accuracy as those of Bates and Damgard and Brugess and Seaton.     

Physical adsorption for non-planar geometries

We propose an approximation V_a(r) for the Van der Waals interaction V(r) between an atom and a non-planar solid. V_a(r) is both simpler to compute than V(r) and of considerably more convenient form. The approximation is found to be quite good except for very large z (the atom-surface separation). In the latter case, our comparison of V_a and V permits one to estimate corrections to V_a.     

The Ruderman-Kittel-Kasuya-Yosida interaction in amorphous La80Au20 alloys with dilute Gd impurities

From magnetization measurements on some amorphous dilute La_80?xGd_xAu₂₀ alloys with x ? 1 we have shown that the magnetic behavior follows the scaling laws of a spin-glass system, characteristic of the 1/r³ dependence of the pairwise interaction. We have also determined the strength of the Ruderman-Kittel-Kasuya-Yosida interaction V(r) = (V₀cos 2k_Fr)/r³, to be V₀ = 0.20 × 10^?37 ergcm³. The corresponding value of the s-f exchange integral is |J_sf| = 0.14 eV, which is compared with values determined from other experiments.     

A Portable NMR Sensor Used for Assessing the Aging Status of Silicone Rubber Insulator

A portable nuclear magnetic resonance (NMR) sensor with an adjustable ‘clamp’ structure is constructed for the noninvasive measurement of the aging status of silicone rubber insulators used in the high-voltage power transmission. The Carr–Purcell–Meiboom–Gill sequence was employed to record the ¹H NMR transverse relaxation curves of silicone rubber insulators with different service times. The decay curves were fitted to mono-exponential and bi-exponential functions. Further data processing of the decay curves was performed with the inverse Laplace transformation for one-dimensional T ₂ distribution analysis, focusing on the mean lifetime of the long T ₂ component (T _{2long mean}). The results demonstrate that an increase in the aging level of the insulator clearly results in a decrease of T _{2long mean}. For comparison, the relative permittivity of the insulator was also measured. It shows the same trend as that of T _{2long mean}. This indicates that the T _{2long mean} relaxation time obtained from our portable NMR sensor can reliably be used as an index to reflect the aging status of silicone rubber insulator.     

The thermochemistry of the hydrogen vanadium bronzes HxV2O5

The enthalpies of formation of seven hydrogen vanadium bronzes, H_xV₂O₅(0<x⩽3.77), prepared at ambient temperature by “hydrogen spillover”, have been determined by solution calorimetry. The enthalpy values obtained for their formation from H₂(g) and V₂O₅(s) at 298.15 K are (in kJ mol⁻¹): H_0.22V₂O₅, −1569.95 ± 1.75; H_0.46V₂O₅, −1589.96 ± 1.69; H_1.43V₂O₅, − 1670.53 ± 1.88; H_1.87V₂O₅, −1700.56 ± 1.58; H_2.79V₂O₅, −1744.23 ± 1.72; H_3.53V₂O₅, −1772.98 ± 2.38; H_3.77V₂O₅, −1781.10 ± 2.27. The stabilities of the compounds towards decomposition, disproportion and oxidation are discussed.     

Structural,optical and magnetic properties of Cu and V co-doped ZnO nanoparticles

Zn_0.98−xCu_xV_0.02O (x=0, 0.01, 0.02 and 0.03) samples were synthesized by the sol–gel technology to dope up to 3% Cu in ZnO. Investigations of structural, optical and magnetic properties of the samples have been done. The results of X-ray diffraction (XRD), transmission electron microscope (TEM) and X-ray photoelectron spectroscopy (XPS) indicated that the V and Cu ions were incorporated into the crystal lattices of ZnO. With Cu doping concentration increasing up to 2 at%, the XRD results showed that all diffraction peaks corresponded to the wurtzite structure of ZnO. Photoluminescence (PL) measurements showed that Zn_0.98−xCu_xV_0.02O powders exhibited that the position of the ultraviolet (UV) emission peak of the samples showed an obvious red-shift and the green emission peak enhanced significantly with Cu doping in ZnVO nanoparticle. Magnetic measurements indicated that room temperature ferromagnetism (RTFM) of Zn_0.98−xCu_xV_0.02O was an intrinsic property when Cu concentration was less than 3 at%. The saturation magnetization (M_s) of Zn_0.98−xCu_xV_0.02O (x=0, 0.01 and 0.02) increased with the increase of the Cu concentration.     

Local density valence band offset in GaAs/AlAs: Role of interface dipole

The valence band offset, ΔE_V ,at the lattice-matched GaAs/AlAs(001) interface is derived from highly precise self- consistent all-electron local density band structure calculations of the (GaAs)_n(AlAs)_n(001) superlattices (with n ⩽ 3). Using the core levels as reference energies, we find that ΔE_V = 0.50 ± 0.05 eV, in very good agreement with recent experimental results (ΔE_V = 0.45 − 0.55 eV). The dependence of ΔE_V on the superlattice thickness is studied and related to the interface charge redistribution which produces an interface dipole potential estimated to be ∼ 0.14 eV.     

The reference potential in the ATA

Precise limitations on the choice of the reference potential for the ATA are investigated, and it is shown that V⁽ⁱ⁾_r?〈V_i〉=O(xy).     

Structure and propagation of two-dimensional,partially premixed,laminar flames in diesel engine conditions

We investigate the influence of inflow velocity (V_in) and scalar dissipation rate (χ) on the flame structure and stabilisation mechanism of steady, laminar partially premixed n-dodecane edge flames stabilised on a convective mixing layer. Numerical simulations were performed for three different χ profiles and several V_in (V_in = 0.2 to 2.5m/s). The ambient thermochemical conditions were the same as the Engine Combustion Network’s (ECN) Spray A flame, which in turn represents conditions in a typical heavy duty diesel engine. The results of a combustion mode analysis of the simulations indicate that the flame structure and stabilisation mechanism depend on V_in and χ. For low V_in the flame is attached. Increasing V_in causes the high-temperature chemistry (HTC) flame to lift-off, while the low-temperature chemistry (LTC) flame is still attached. A unique speed S_R associated with this transition is defined as the velocity at which the lifted height has the maximum sensitivity to changes in V_in. This transition velocity is negatively correlated with χ. Near $V_{in}=S_R$ a tetrabrachial flame structure is observed consisting of a triple flame, stabilised by flame propagation into the products of an upstream LTC branch. Further increasing the inlet velocity changes the flame structure to a pentabrachial one, where an additional HTC ignition branch is observed upstream of the triple flame and ignition begins to contribute to the flame stabilisation. At large V_in, the LTC is eventually lifted, and the speed at which this transition occurs is insensitive to χ. Further increasing V_in increases the contribution of ignition to flame stabilisation until the flame is completely ignition stabilised. Flow divergence caused by the LTC branch reduces the χ at the HTC branches making the HTC more resilient to χ. The results are discussed in the context of identification of possible stabilisation modes in turbulent flames.     

Asymptotic properties of the solutions of a differential equation appearing in QED and QCD

Stimulated by the study described in the preceding paper, we establish the asymptotic behaviour of the ratio h′(0)/h(0) for g → ∞, where h(r) is a solution, vanishing at infinity, of the differential equation h″(r) = igω(r)h(r) on the domain 0 ≤ r ≤ ∞ and ω(r) = (1 − √rK₁(√r))/r. Some results are valid for more general ω's.     

Approach to saturation of the magnetization of dilute AuFe alloys

We present a reinterpretation of our recent measurements of the magnetic properties of some dilute AuFe alloys. We find that the observed approach to saturation of the magnetization for these AuFe alloys can be understood if both single-impurity (Kondo) effects and effects due to interactions between impurities via the Rudeman-Kittel-Kasuya-Yosida (RKKY) interaction, V(r) = (V₀ cos 2k_Fr)/r³, are properly included in the analysis. The analysis yields for the strength of the RKKY interaction V₀ = (1.1 ± 0.3) × 10^-36ergcm³, for the s-d exchange parameter |J| = (1.9 ± 0.3) eV, and for the Kondo temperature T_K = (0.8 ± 0.1) K. We conclude that mean free path effects do not significantly influence the observed approach to saturation of the magnetization for the AuFe alloys studied.     

Thermodynamics of nonstoichiometric multicomponent uranium oxides

A simple graphic method is described for calculating the thermodynamic properties of U and other metals in a nonstoichiometric r-component (r ⩾ 3) uranium oxide U_1-yM′_y3M_y4… O_2+x from the known oxygen potential. Only one set of graphic integration and (r − 2) sets of graphic differentiation are needed. Experimental data in an iso-x (r − 1)-component subsystem for which the oxygen potential is a linear function of y_i(i = 3,4,…, r) may easily be used to give a more accurate integration constant for the calculation. Sample calculations have been done for the U_t-yGd_yO_2+x solid solutions. This method can also be applied to other nonstoichiometric multicomponent solid compounds of importance in nuclear technology such as thorium-based and plutonium-based fuels.     

Acceleration of magnetic dipoles by a sequence of current-carrying turns

Magnetic dipoles are accelerated by a running gradient of the magnetic field that is produced by sequentially energizing current-carrying turns. Magnetic dipoles d _sh = 60 mm in diameter and l _tot = 1 m in length are gasdynamically preaccelerated to velocity V _in = 1 km/s, with which they are injected into the main accelerator. The turnover of the dipoles in the field of an accelerating pulse is prevented and focusing of dipoles is provided by directing the dipoles into a titanium tube. The weight of the dipoles is m = 2 kg, and they acquire final velocity V _fin = 5 km/s over acceleration length L _acc = 300 m.     

Variation of RKKY interaction strength in dilute AuFe alloys

From measurements of the magnetic properties of some dilute AuFe alloys we find that V₀, the strength of the Ruderman-Kittel-Kasuya-Yosida interaction, V(r) = (V₀ cos 2k_Fr)/r³, decreases rapidly from V₀ = 11.9 × 10^-36 erg cm³ at n = 42 ppm Fe to 1.03 × 10^-36 erg cm³ at 6050 ppm Fe. We suggest that the observed decrease of V₀ is due to self-damping of the RKKY oscillations, and discuss the significance of this decrease for the interpretation of other experiments on AuFe.     

The p-40Ca and n-40Ca mean fields from the iterative moment approach

The real part V(r; E) of the p-⁴⁰Ca and n-⁴⁰Ca mean fields is extrapolated from positive towards negative energies by means of the iterative moment approach, which incorporates the dispersion relation between the real and imaginary parts of the mean field. The potential V(r; E) is the sum of a Hartree-Fock type component V^HF, (r; E) and a dispersive correction δV(r; E); the latter is due to the coupling of the nucleon to excitations of the ⁴⁰Ca core. The potentials V(r; E) and V_HF(r; E) are assumed to have Woods-Saxon shapes. The calculations are first carried out in the framework of the original version of the iterative moment approach, in which both the depth and the radius of the Hartree-Fock type contribution depend upon energy, while its diffuseness is constant and equal to that of V(r; E). The corresponding extrapolation towards negative energies is somewhat sensitive to the detailed parametrization of the energy dependence of the imaginary part of the mean field, which is the main input of the calculation. Moreover, the radius of the calculated Hartree-Fock type potential then increases with energy, in contrast to previous findings in ²⁰⁸Pb and ⁸⁹Y. A new version of the iterative moment approach is thus developed in which the radial shape of the Hartree-Fock type potential is independent of energy; the justification of this constraint is discussed. The diffuseness of the potential V(r; E) is assumed to be constant and equal to that of V_HF(r; E). The potential calculated from this new version is in good agreement with the real part of phenomenological optical-model potentials and also yields good agreement with the single-particle energies in the two valence shells. Two types of energy dependence are considered for the depth U_HF(E) of the Hartree-Fock type component, namely a linear and an exponential form. The linear approximation is more satisfactory for large negative energies (E < −30 MeV) while the exponential form is better for large positive energies (E > 50 MeV). This is explained by relating the energy dependence of U_HF(E) to the nonlocality of the microscopic Hartree-Fock type component. Near the Fermi energy the effective mass presents a pronounced peak at the potential surface. This is due to the coupling to surface excitations of the core and reflects the energy dependence of the potential radius. The absolute spectroscopic factors of low-lying single-particle excitations in ³⁹Ca, ⁴¹Ca, ³⁹K and ⁴¹Sc are found to be close to 0.8. The calculated p-⁴⁰Ca and n-⁴⁰Ca potentials are strikingly similar, although the two calculations have been performed entirely independently. The two potentials can be related to one another by introducing a Coulomb energy shift. Attention is drawn to the fact that the extrapolated energy dependence of the real part of the mean field at large positive energy sensitively depends upon the assumed behaviour of the imaginary part at large negative energy. Yet another version of the iterative moment approach is introduced, in which the radial shape of the HF-type component is independent of energy while both the radius and the diffuseness of the full potential V(r; E) depend upon E. This model indicates that the accuracy of the available empirical data is probably not sufficient to draw reliable conclusions on the energy dependence of the diffuseness of V(r; E).